```PYTHON
# DO *NOT* WRITE YOUR NAME TO MAINTAIN ANONYMITY FOR PLAGIARISM DETECTION
# Prompts the user for an arity (a natural number) n and a word.
# Call symbol a word consisting of nothing but alphabetic characters
# and underscores.
# Checks that the word is valid, in that it satisfies the following
# inductive definition:
# - a symbol, with spaces allowed at both ends, is a valid word;
# - a word of the form s(w_1,...,w_n) with s denoting a symbol and
# w_1, ..., w_n denoting valid words, with spaces allowed at both ends and
# around parentheses and commas, is a valid word.
import sys
def is_valid(word,arity):
high =0
result = []
tmp = []
for cin word:
if c ==')':
high -=1
if high ==arity -1:
result.append(''.join(tmp))
tmp = []
if high ==arity:
if c ==',':
result.append(''.join(tmp))
tmp = []
else:
tmp.append(c)
elif high >arity:
tmp.append(c)
if c =='(':
high +=1
if tmp:
result.append(''.join(tmp))
return result
return False
# REPLACE THE RETURN STATEMENT ABOVE WITH YOUR CODE
try:
arity =int(input('Input an arity : '))
if arity <0:
raise ValueError
except ValueError:
print('Incorrect arity, giving up...')
sys.exit()
word =input('Input a word: ')
if is_valid(word, arity):
print('The word is valid.')
else:
print('The word is invalid.')
```
例子：
QUIZ 3
COMP9021 PRINCIPLES OF PROGRAMMING
$ python3 quiz_3.py
Input an arity : 0
Input a word: f_1
The word is invalid.
$ python3 quiz_3.py
Input an arity : 0
Input a word: ()
The word is invalid.
$ python3 quiz_3.py
Input an arity : 0
Input a word: function_of_arity_one(hello)
The word is invalid.
$ python3 quiz_3.py
Input an arity : 1
Input a word: f)
The word is invalid.
$ python3 quiz_3.py
Input an arity : 1
Input a word: f[a]
The word is invalid.
$ python3 quiz_3.py
Input an arity : 2
Input a word: f(a, g(b))
The word is invalid.
$ python3 quiz_3.py
Input an arity : 3
Input a word: constant
The word is invalid.
$ python3 quiz_3.py
Input an arity : 3
Input a word: f((a,b,c))
The word is invalid.
$ python3 quiz_3.py
Input an arity : 3
Input a word: f(g(a,a), f(a,b))
The word is invalid.
$ python3 quiz_3.py
Input an arity : 3
Input a word: f(g(a,b,c),g(a,b,c),g(a,b,c)
The word is invalid.
$ python3 quiz_3.py
Input an arity : 3
Input a word: f(a, g(a, b, f(a,b,c)), b, c)
The word is invalid.
Date: Term 3, 2020.
2 COMP9021 PRINCIPLES OF PROGRAMMING
$ python3 quiz_3.py
Input an arity : 0
Input a word: a
The word is valid.
$ python3 quiz_3.py
Input an arity : 1
Input a word: function_of_arity_one(hello)
The word is valid.
$ python3 quiz_3.py
Input an arity : 2
Input a word: F(g(a,a), f(a,b))
The word is valid.
$ python3 quiz_3.py
Input an arity : 3
Input a word: ff(ff(ff(a,b,ff(aa,bb,cc)) , b , ff(a,b,c)) , b , ff(a,ff(a,b,c),c))
The word is valid.
$ python3 quiz_3.py
Input an arity : 4
Input a word: f(a, FF(a, b, fff(a, b, c, FfFf(a,b,c,d)), FfFf(a,b,c,d)), c,d)
The word is valid.
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